In Resonance of Fate, you can get colored hexes primarily as a drop from human enemies or as a bonus prize after specific overworld battles. Once you figure out where to get each drop, it becomes not too difficult to harvest them... until you advance the plot. In later chapters, enemies in battles are replaced by much more powerful encounters, which not only replaces the drops of the enemies themselves but also affects that bonus prize in overworld battles. This makes it much harder to get some of the earlier hexes when you're approaching the late game.

My question is, what are the most efficient ways to harvest the different colored energy hexes throughout the game? Ideally, I'd like to know not just where they are best found, but during what chapters I can use those sources and what alternatives are available after those points.

In particular, the purple energy hex in the diamond shape seems to be almost completely absent at the stage of the game we're at. It is only ever dropped by a single normal enemy (the Outcast STG in the Hughes Power Station), which does still occasionally spawn but is more often replaced by the more annoying Mask Raiders who do not drop purples. Unless we somehow skipped over it, we also have not found any Arena battle that drops purple hexes. And all of the encounters where they used to be dropped (primarily on Level 6) have been replaced with more difficult battles that prefer to give greens instead.

2 Answers
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The Forrest of Idols is an excellent place to farm Yellow U-shaped hexes, starting in chapter 3, as I recall (It has been a while since I played). You can farm there at any time the area opens up. I would recommend filling the area with yellow hexes before entering the main dungeon there to get the terminal bonuses.